Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Numerical Solution of PDEs on Parallel Computers Utilizing Sequential Simulators
ISCOPE '97 Proceedings of the Scientific Computing in Object-Oriented Parallel Environments
International Journal of High Performance Computing Applications
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We study the electrical field in the human body, generated by the ventricular muscle, by means of numerical simulations. The involved mathematical model consists of two partial differential equations (PDEs) that are also coupled with a system of ordinary differential equations (ODEs). Following the strategy of operator-splitting, we have devised an efficient numerical algorithm that carries out a simulation stepwise in time. At every time level, the ODE system is solved before a parabolic PDE, and then an elliptic PDE. The main focus of this paper is on the transformation of an existing sequential simulator into a parallel simulator that runs on multiprocessor platforms. Two important numerical ingredients used in the resulting parallel simulator are overlapping domain decomposition and multigrid, which together ensure good numerical efficiency. We also explain howob ject-oriented programming techniques enable the software parallelization in a simple and structured manner. In addition, we study the performance of the parallel simulator on different multiprocessor platforms.